The areas of two similar triangles are 200 an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For two similar triangles,the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.Let the areas be $A_1 = 20

Vedclass · Accepted Answer

$5:4$

Vedclass · Answer

(D) For two similar triangles,the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.Let the areas be $A_1 = 200$ and $A_2 = 128$.Let the corresponding altitudes be $h_1$ and $h_2$.According to the theorem,$\frac{A_1}{A_2} = \left(\frac{h_1}{h_2}\right)^2$.Substituting the values: $\frac{200}{128} = \left(\frac{h_1}{h_2}\right)^2$.Simplifying the fraction: $\frac{200}{128} = \frac{100}{64} = \frac{25}{16}$.Therefore,$\left(\frac{h_1}{h_2}\right)^2 = \frac{25}{16}$.Taking the square root on both sides: $\frac{h_1}{h_2} = \sqrt{\frac{25}{16}} = \frac{5}{4}$.Thus,the ratio of their corresponding altitudes is $5:4$.

The areas of two similar triangles are $200$ and $128$. Then,the ratio of their corresponding altitudes is.....

Similar Questions

If $\triangle ABC \sim \triangle EDF$ and $\triangle ABC$ is not similar to $\triangle DEF$,then which of the following is not true?

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 5$,$MB = 8$ and $AN = 10$,then $NC = \dots$

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

In rhombus $PQRS$,$PR = 9$ and $QS = 12$. Find the perimeter of rhombus $PQRS$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 3x - 1$,$MB = 2x + 1$,$AN = 3x + 1$ and $NC = 5x + 1$,find the value of $x$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module